CMAC neural network as an SVM with B-spline kernel functions

Abstract

In measurement systems, there is an often need Cerebellar Model Articulation Controller (CMAC) neural network has some attractive features. The most important ones are its extremely fast learning capability and the special architecture that lets effective digital hardware implantation possible. All these properties may be important in measurement systems, e.g. in system modeling or in complex sensor's system, etc. Although the CMAC architecture was proposed in the middle of the seventies, several open questions have been left even for today. Among them the most important ones are about its modeling and generalization capabilities. The limits of fits modeling capability were addressed in the literature and recently a detailed analysis of its generalization properties was given. The results show that there are significant differences between the one-dimensional and the multidimensional versions of CMAC. The modeling capability of a multidimensional network is inferior to that of the one-dimensional one. This paper discusses the reasons of this difference and suggests a new interpretation of CMAC. This interpretation is based on kernel machines. The paper shows that a one-dimensional binary CMAC can be considered as a kernel machine with linear B-spline kernel function. However, this close relation cannot be found in multidimensional case. The paper proposes a version of multidimensional CMAC, which - similarly to the one-dimensional case - can be considered as a kernel machine. The paper introduces this interpretation and details its most important advantages.